By Brian T. Sutcliffe (auth.), Professor Dr. Zvonimir B. Maksić (eds.)
"Imagination and sensible guesswork are robust tools for buying medical wisdom . . . " 1. H. van't Hoff The final many years have witnessed a swift development of quantum chemistry and a huge bring up within the variety of very actual ab initio calculations of the digital constitution of molecules yielding result of admirable accuracy. This dramatic development has opened a brand new degree within the quantum mechanical description of subject on the molecular point. within the first position, hugely actual effects supply serious assessments of the quantum mecha nics. Secondly, smooth quantitative computational ab initio equipment should be synergetically mixed with a number of experimen tal concepts hence allowing designated numerical characterization of molecular homes greater than ever expected previous. besides the fact that, the position of idea isn't exhausted in disclosing the basic legislation of Nature and construction of ever expanding units of knowledge of excessive accuracy. It has to supply also a way of systematization, acceptance of regularities, and ratio nalization of the myriads of verified proof heading off during this manner whole chaos. extra difficulties are represented by way of molecular wavefunctions supplied through the fashionable high-level computational quantum chemistry tools. They contain, in precept, all of the info on molecular procedure, yet they're so immensely advanced that can't be instantly understood in easy and bodily significant phrases. either one of those elements, categorization and interpretation, demand conceptual versions which could be ideally pictorial, obvious, intuitively attractive and well-founded, being occasionally worthy for semi quantitative purposes.
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Extra resources for Atomic Hypothesis and the Concept of Molecular Structure
Another difficulty that occurs in the Eckart approach, but is not peculiar to that approach, arises from the requirements of permutational invariance and might perhaps have been anticipated from the previous discussion of spaced-fixed coordinates. g. ) that in the Eckart approach only permutations that correspond to point group operations on the framework geometry of the problem can be realised without upsetting the rotation-vibration separation that makes the Eckart approach so attractive.
If the vibration rotation separation spoken of earlier as characteristic of the Eckart approximation is realised explicitly in the present context then the wave function from Eqs. 23) Here Ij;(z, qo) is the electronic wave function evaluated at the equilibrium framework geometry qo and the ck are the coefficients that determine the angular functions appropriate to the equilibrium geometrical structure of the molecule (what kind of top it is). It can now be seen however that the separation, Eq. 23), must be spoiled by virtue of the transformations, Eq.
In particular in all the old quantum theory work it had been assumed that the nuclear motion could be treated classically and that to all intents and purposes the chemist's molecular model could be used to describe the "equilibrium geometry" of a molecule. Indeed these notions were at the heart of early attempts to account for molecular spectra in the old quantum theory. Thus when Heitler and London applied the new quantum mechanics to the Hz molecule in 1927 they did so against this background.